On the electric current from electrodes in a magnetized semiconductor film

The problem on the electric current from electrodes in a magnetized semiconductor film is reduced to the skew derivative problem for the Laplace equation outside cuts in a plane. The problem for the Laplace equation is studied under different conditions at infinity, which have a certain physical meaning. With the help of potential theory, the skew derivative problem is reduced to a Fredholm integral equation of the second kind, which is uniquely solvable. The Neumann problem for the Laplace equation in the exterior of cuts in a plane is a particular case of our problem.